The Black Caps extended their overnight 338 for six to 454 for eight declared, scoring 116 runs in just 16 overs on Monday before captain Brendon McCullum called a halt.
That left England needing 455 to win.
The most any side have made in the fourth innings to win a Test is the West Indies' 418 for seven against Australia at St John's, Antigua, in 2002/03.
England's corresponding record is 332 for seven against Australia at Melbourne back in 1928/29.
Both Adam Lyth, who scored a maiden Test hundred in the first innings, and skipper Alastair Cook, who in the first innings became England's highest run-scorer in Tests, were 15 not out.
When McCullum declared there were still a minimum 171 overs left in the match, leaving England to score at a modest rate of 2.66 runs per over for victory.
New Zealand were unlucky to be 1-0 behind in this two-match series after scoring more than 700 runs and taking 20 wickets in the first Test at Lord's yet still going down to a 124-run defeat.
Mark Craig, 15 not out overnight, was dropped on 23 when a diving Stuart Broad at mid-off failed to hold a tough chance off James Anderson.
But Anderson's second delivery with the new ball removed Watling for 120, the ball taking the shoulder of the bat before third slip Joe Root held a fine catch to end the batsman's 163-ball innings, including 15 fours and a six.
England had missed several slip catches this series and their cause was not helped when Ian Bell failed to move for a chance offered by Tim Southee off Anderson.
The big-hitting Southee fell for 40, off just 24 balls, when he drove off-spinner Moeen Ali to Anderson at long-on.
But it made little difference with New Zealand hammering Broad, who repeatedly bowled too short and, like many of his team-mates, didn't use the yorker, for 19 runs in the last over before the declaration.
Craig drove a back-of-a-length ball down the ground for six and tailender Mark Henry struck two more of his own, ending the innings with a pull that sailed high over deep square leg.
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